{"id":"41505d65-bb2d-476f-a020-0737db97df70","arxiv_id":"2502.05921","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"A three-stage hierarchical beam training method for pinching-antenna systems cuts training overhead from over a million scans to about 50 while keeping data rates near the phase-aligned upper bound.","lead":"This paper proposes beam training schemes for pinching-antenna systems, a new antenna architecture where small dielectric particles on a waveguide act as antennas. The schemes use a scalable codebook and a three-stage search to find good antenna positions with far less training overhead than an exhaustive scan, which matters if pinching antennas become part of 6G networks.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The overhead/rate claim rests on perfectly controllable continuous antenna placement; discrete pinching granularity or waveguide-phase error can make codewords unrealizable and is not stress-tested.","rationale":"The reader's weakest-assumption analysis correctly identifies the ideal continuous-activation model in Section II-A as the load-bearing point: the codebook construction S1–S5, the received-signal model in Eq. (1), and all three stages of Algorithm 2 depend on being able to place pinching antennas at exact continuous locations with exactly known waveguide phase. My stress-test agrees with this and sharpens it by specifying a quantitative failure mode: quantization or phase error makes the generated codewords unrealizable, so the RSS-based hierarchical pruning in Stages 1 and 2 is no longer evaluating the intended codewords and may select the wrong sub-region. The paper provides neither a sensitivity analysis nor Monte Carlo evidence to show the 48-slot overhead survives such imperfections. This does not invalidate the mathematical ideal-case contribution, but it does mean the central overhead/rate claim is conditional on hardware that is not demonstrated. Since the reader already returned CONDITIONAL for essentially this reason, no verdict change is needed; the appropriate final assessment remains conditional on validation of the ideal-activation assumption.","tokens_in":22019,"tokens_out":16022,"duration_ms":181289,"concrete_test":"Re-run the SWSU simulation of Algorithm 2 with antenna positions quantized to a feasible grid of spacing delta in {lambda/4, lambda/2, lambda} and with zero-mean Gaussian errors added to theta_n of std sigma_theta in {5 deg, 10 deg, 20 deg}. For each setting, run 100 random user locations, keep the same 48-slot training budget, and record the median rate gap to the phase-aligned upper bound. If the median gap exceeds about 1 bit/s/Hz, or if extra training layers are needed to recover the gap shown in Fig. 8, then the claimed overhead reduction is not robust to realistic pinching-antenna hardware.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section II-A states the ideal scenario that pinching antennas can be activated perfectly at any desirable location with exactly known waveguide phase. Every codeword in the scalable codebook is generated by solving the phase-alignment equations S1–S5, which require arbitrary position resolution and exact knowledge of theta_n in Eq. (1). The three-stage training then assumes these codewords are physically realizable: Stage 1 prunes the x-range based on single-antenna RSS, Stage 2 prunes the y-range using phase-aligned multi-antenna codewords, and Stage 3 performs the final exhaustive refinement. If real hardware offers only discrete placement positions, or if the waveguide phase has uncertainty, then no codeword satisfies mod{...}=0 exactly, the measured received power no longer corresponds to the intended codeword, and the hierarchical pruning can lock onto the wrong region. Because Table I and Figs. 7–10 are generated for a single fixed user location with no sensitivity sweep over placement granularity or phase error, the central claim that 48 slots suffice with 'reasonable rate performance' is only established under an idealized, perfectly calibrated hardware model.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes beam-training designs for pinching-antenna systems (PASS) in three scenarios: single-waveguide-single-user (SWSU), single-waveguide-multi-user (SWMU), and multi-waveguide-multi-user (MWMU). For each scenario it introduces a scalable codebook generated by solving phase-alignment conditions (S1-S5), and a three-stage hierarchical beam training (3SBT) scheme that first estimates the user's x-coordinate with a single antenna, then refines the y-coordinate with an increasing number of antennas, and finally performs a partial exhaustive search. The paper claims that this reduces training overhead from 2^20 slots to 48 slots in the SWSU setup of Table I while maintaining reasonable rate performance, and that dynamic pinching antennas outperform fixed-location pinching antennas and conventional arrays. Numerical results for a single fixed geometry are presented at 28 GHz and 5 GHz.","tokens_in":22219,"tokens_out":10398,"duration_ms":109571,"significance":"If the claims hold, the paper makes a useful contribution: it gives a systematic, scalable codebook construction and a hierarchical training protocol for a new antenna architecture, with a correct and easily verified overhead count in Table I (48 vs. 2^20 slots for the SWSU case). The extension to NOMA-based SWMU and to partially-connected hybrid beamforming in MWMU broadens the applicability. However, the validation is currently much narrower than the claims: all simulations are deterministic and use a single user geometry per scenario, and the underlying model assumes ideal continuous placement and perfect knowledge of waveguide phase. The central overhead reduction is a counting argument and is sound; the rate-performance claim is plausible but is not yet supported by sensitivity analysis or statistical results.","major_comments":[{"comment":"The codebook construction S1-S5 requires exact antenna positions satisfying mod{2π/λ |ψ_f - ψpin_n| + θ_n, 2π}=0, which presupposes continuous placement resolution and perfect knowledge of the waveguide phase θ_n. This ideal assumption, stated in Section II-A, is not stress-tested anywhere in Section V: all figures are generated under the same model, and no sweep over placement granularity or phase error is reported. Since a placement or phase error changes the received power of every codeword and can mislead the hierarchical decisions in Algorithm 2, the central claim that 3SBT achieves reasonable rate with low overhead is currently only established for an idealized, perfectly calibrated hardware model. The authors should add a robustness study or explicitly reframe the claims as ideal-theoretic.","section":"Section II-A, Eq. (1), and S1-S5"},{"comment":"The rate-performance claim is supported by a single deterministic user location, ψU=(5,4,0), with fixed L1, L2, K, and dES settings. There is no averaging over user positions or channel realizations, and the paper does not plot the rate achieved by the 2D exhaustive-search baseline of Table I; Fig. 8 compares against the phase-aligned upper bound, which is a different reference. To make the comparison complete, please include an exhaustive-search rate curve and report statistics (mean/percentiles) over multiple user geometries, and state whether the 48-slot overhead always identifies the same codeword as the exhaustive search.","section":"Section V-A, Figs. 7-8 and Table I"},{"comment":"In the separated user training stage, the received signal at Um contains contributions from all antenna clusters because the same waveguide carries the superimposed NOMA signal, but the paper assumes that large-scale fading makes the desired cluster's signal dominate. This assumption is stated without a quantitative condition or numerical validation. If the clusters are not sufficiently separated, the measured |r_m| used for hierarchy decisions is corrupted by inter-cluster interference, and Stage 1 can select a wrong sub-range. Please provide a quantitative condition (e.g., minimum inter-user distance or power ratio) under which the assumption holds, and show the sensitivity of Stage-1 accuracy to this parameter.","section":"Section III-B1, Stage 1 of Algorithm 3"}],"minor_comments":[{"comment":"The sentence \"Sections II, III and IV focus on SWSU-PASS, SWSU-PASS and SWSU-PASS respectively\" should read SWSU, SWMU, and MWMU.","section":"Section I, final paragraph"},{"comment":"In the formula N' = min{2^{l+1-L1}, N}, clarify that l continues from L1+1 when the second while loop begins; otherwise the exponent is undefined at the start of the stage.","section":"Algorithm 2, Stage 2"},{"comment":"The waveguide phase term uses a single feed point ψpin_0, but in Section V-C each waveguide has a different feed point; please define ψpin_0,q for each waveguide or state that a common reference is used.","section":"Eq. (20) and Section V-C"},{"comment":"\"Preprint\" is misspelled as \"Prepint\" in both references.","section":"References [8] and [9]"},{"comment":"The 5 GHz curve does not converge, and the text attributes this to larger guard distances and discretization errors; a sentence explaining the connection between wavelength, guard distance (Δ=λ/2), and phase error would aid the reader.","section":"Fig. 8"},{"comment":"For SWMU with M=3, the proposed overhead is 4192 slots, which is much larger than the M=2 value; the paper should note that Stage 3 grows as the product of per-user candidate counts and discuss complexity for larger M.","section":"Table I"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is within the scope of the journal and the basic overhead-reduction idea is sound. My main reservation is that the practical claims outrun the validation: the paper relies on an ideal continuous-placement model and single-geometry deterministic simulations. I would not reject the paper, but the revision should include robustness studies (placement granularity, phase error, multiple user positions) and a direct rate comparison with the exhaustive-search baseline. The self-citations to the authors' prior PASS papers are relevant and appropriate."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this is a solid first paper on beam training for pinching-antenna systems. The key idea — codewords as physical antenna locations generated by phase-matching equations, rather than beamforming weight vectors — is genuinely new and makes the hierarchical training scheme non-trivial. The overhead reduction from 2^20 to 48 slots in the simulated setup is a straightforward count and checks out. The 28 GHz rate converging to the phase-aligned bound (Fig. 8) supports the rate claim for the case shown.\n\nWhat's good: the scalable codebook is a clean construct; adding sampling points or antennas is incremental. The three-stage training is well explained and Algorithm 2 is implementable. The SWMU and MWMU extensions are natural, and the NOMA reclustering step is a sensible way to handle close users. The paper also honestly flags that the ideal-activation assumption is an assumption (Section II-A).\n\nSoft spots, in order of severity. First, the load-bearing idealization: continuous, perfectly calibrated pinching antenna placement with exactly known waveguide phase. The codewords are solutions to mod{...}=0 equations; if hardware has discrete placement or phase error, the codewords are not realizable, and the hierarchical pruning could lock onto the wrong region. The paper does no sensitivity analysis over placement granularity or phase error, and all simulations are single-run deterministic. This is a real gap, but it is a standard gap for a first system paper — the authors state the assumption openly and the math is consistent within it. Second, the multi-user analysis assumes inter-cluster interference is negligible, which is reasonable for the well-separated users simulated but not proven. Third, the codebook's near-optimality is asserted via construction, not proved; given the exhaustive search in stage 3, the residual error is bounded by the final grid spacing, so this is a minor concern.\n\nThe citation pattern looks fine; the self-citations are to the papers that introduced the PASS channel model, and the prior near-field beam training work is acknowledged. No invented entities, just two free parameters (reclustering threshold and guard distance) set without sensitivity sweeps.\n\nWho this is for: researchers working on pinching antennas or near-field beam training for reconfigurable antennas. It deserves a serious referee. The weaknesses are addressable in revision — add a hardware-imperfection model and Monte Carlo results — but the core contribution is clear and new.","headline":"A legitimate first paper on beam training for pinching antennas: the codebook-as-antenna-locations idea is new, the overhead reduction is real, and the main weakness is the untested ideal-hardware assumption rather than a flawed core.","tokens_in":22759,"tokens_out":1688,"would_cite":true,"duration_ms":17418,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"For pinching-antenna wireless systems, this paper proposes a three-stage codebook-based beam training scheme that cuts training overhead to 48 slots versus $2^{20}$ for exhaustive search, while keeping rates close to the phase-aligned…","keywords":["beam training","pinching-antenna systems","codebook design","near-field communications","NOMA","hybrid beamforming","hierarchical training","training overhead"],"falsifier":"Build or simulate a pinching-antenna setup where activation positions are quantized to a grid of spacing $\\delta$ (for example $\\lambda/10$) and the waveguide propagation constant has a few percent uncertainty; run the proposed 3SBT at 28 GHz and compare the final rate to the phase-aligned bound. If the gap does not shrink to near zero as training layers increase while the ideal-continuous codebook does, the perfect-placement assumption is the load-bearing part of the claim.","tokens_in":1945,"feed_emoji":"📡","tokens_out":2758,"duration_ms":92853,"temperature":0.7,"pith_summary":"This paper tries to establish that pinching-antenna systems can align beams to users without full channel estimation, by treating the physical locations of activated antennas as the beamforming design. It proposes a scalable codebook of antenna-location patterns and a three-stage beam training scheme that first localizes the user coarsely along one axis, then refines it with more antennas, then finishes with a small exhaustive search. The claimed payoff is a dramatic cut in training overhead, from $2^{20}$ slots for a two-dimensional exhaustive search to 48 slots in the simulated single-user setup, while the achievable rate approaches the phase-aligned upper bound at 28 GHz. The same codebook idea is extended to multiple users on one waveguide using NOMA and to multiple waveguides with hybrid beamforming, where choosing which waveguide serves which user adds another degree of freedom. A sympathetic reader would take the paper as showing that dynamic pinching antennas turn beam training into a location-estimation problem that can be solved cheaply and scalably.","feed_headline":"Pinching antennas find users in 48 slots, not a million","feed_subtitle":"A three-stage codebook search cuts training overhead from about a million slots to 48 while rates stay near ideal.","key_machinery":"The central object is the scalable codebook, where each codeword is not a complex beamforming weight vector but a list of physical locations for the $N$ activated pinching antennas along the waveguide. For a given sampling point $\\psi_f$, steps S1-S5 generate these locations by solving the modulo phase-alignment condition that combines free-space propagation phase and in-waveguide phase $\\theta_n$, while maintaining a guard distance $\\tilde{\\Delta}$. The three-stage beam training scheme, 3SBT, then exploits this codebook: stage one activates a single antenna to estimate the user's x-coordinate from received signal strength, stage two increases the antenna count to refine the y-coordinate, and stage three runs an exhaustive search over a small remaining region. Because the codebook is scalable, new sampling points and additional antennas can be added without regenerating existing codewords, which is what makes the low-overhead hierarchy possible and lets the same design extend to multi-user and multi-waveguide cases.","core_discovery":"The paper's central claim is that beam training in a pinching-antenna system can be reduced to locating the user and placing antennas at the positions that make all signal phases align at the user. For a sampled user point $\\psi_f$, the scalable codebook places each activated antenna at the first position along the waveguide, alternating outward from the point closest to the user, that satisfies the phase condition $\\mathrm{mod}\\{\\frac{2\\pi}{\\lambda}|\\psi_f-\\tilde{\\psi}^{\\mathrm{pin}}_n|+\\theta_n,2\\pi\\}=0$, with a guard distance $\\tilde{\\Delta}$ between antennas to avoid coupling. The three-stage scheme uses one antenna for a coarse x-coordinate estimate, an increasing number of antennas for y-direction phase matching, and a final partial exhaustive search over the surviving rectangle. In the simulated SWSU setup this takes $K(L_1+L_2)+K_1K_2=48$ training slots instead of $K^{L_1+L_2}K_1K_2=2^{20}$ for a 2D exhaustive search, and the rate gap to the phase-aligned bound shrinks to nearly zero at 28 GHz as training layers increase. The same codebook structure is adapted to SWMU scenarios with NOMA and to MWMU scenarios with partially-connected hybrid beamforming, with simulations showing dynamic pinching antennas outperforming fixed-location pinching antennas and conventional arrays.","pith_inferences":["If continuous antenna placement is relaxed to a discrete grid, the codebook generation steps could be rounded to the nearest feasible positions; the hierarchical training would still work, but the achievable-rate gap would then depend on the grid spacing, which is a testable extension the paper does not run.","The scheme's coarse first stage relies on received signal strength scaling with distance, which is most reliable in line-of-sight near-field settings; in rich multipath or heavily blocked environments the one-antenna localization step could point to the wrong x-region and the later stages would inherit that error.","The multi-user and multi-waveguide results use equal power splitting and no digital precoding optimization, so jointly optimizing power allocation and precoding with the codebook-based training is a natural next step that could push sum rates above the reported equal-power curves.","The overhead comparison assumes the codebook, once generated, can be reused; in a mobile setting the hierarchical first stage could be run periodically to track the user, with the later stages reusing the stored codewords, but tracking behavior is not studied in the paper."],"forward_implications":["Pinching-antenna systems can be trained with tens of slots instead of roughly a million, removing a major barrier to using them without explicit channel estimation.","The same scalable codebook supports multi-user NOMA training, with per-user antenna clusters and a joint exhaustive stage, so the multi-user overhead grows from one user's cost to a sum over users plus a product of small refinement subranges.","Multi-waveguide PASS adds a new degree of freedom, waveguide selection, and the paper's Lemma 1 states that each user gets the largest received signal strength when all its antennas sit on the closest waveguide clustered around the point nearest the user.","Dynamic pinching antennas outperform fixed-location pinching antennas and conventional uniform linear arrays at equal power in the simulations, with the gain growing as the number of activated antennas increases.","Phase-alignment performance is better at higher carrier frequencies, because the shorter wavelength makes the codebook's discretization errors smaller relative to the user distance."],"supporting_citations":[{"why":"Introduces the pinching-antenna concept that the paper's system model builds on.","marker":"[7]"},{"why":"Supplies the pinching-antenna channel model used in Eq. (1) and the phase-aligned rate upper bound used as a benchmark in the simulations.","marker":"[9]"},{"why":"Provides the spherical-wave near-field channel model in which CSI depends on both angle and distance, motivating the two-dimensional exhaustive search baseline.","marker":"[12]"},{"why":"Supplies the near-field hierarchical 2D beam-training method that the proposed scheme adapts to single-waveguide PASS.","marker":"[13]"},{"why":"Supplies the two-stage angular-and-distance beam-training structure echoed in the three-stage design.","marker":"[14]"},{"why":"Supplies the hierarchical codebook multiuser beam-training idea that justifies avoiding direct channel estimation in the multi-waveguide case.","marker":"[22]"}],"fun_headline_variants":["Pinching antenna beam training cuts search to 48 slots","Three-stage beam training: 48 slots for pinching antennas","Pinching antennas: dynamic placement finds users in 48 slots","Beam training for pinching antennas: 48 slots over a million","Pinching antennas: one user, 48 training slots"],"cache_read_input_tokens":24832,"weakest_assumption_plain":"The paper assumes a pinching antenna can be activated perfectly at any exact point along the waveguide and that the waveguide phase delay at that point is known precisely, so the codeword positions computed from the modulo phase condition are physically realizable.","fun_headline_variants_meta":{"raw":{"variants":["Pinching antenna beam training cuts search to 48 slots","Three-stage beam training: 48 slots for pinching antennas","Pinching antennas: dynamic placement finds users in 48 slots","Beam training for pinching antennas: 48 slots over a million","Pinching antennas: one user, 48 training slots"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001302,"raw_usage":{"total_tokens":5395,"prompt_tokens":1116,"completion_tokens":4279,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":732,"completion_tokens_details":{"reasoning_tokens":4193}},"tokens_in":732,"tokens_out":4279,"duration_ms":27462,"temperature":1.0,"reasoning_tokens":4193,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-08T17:23:45.694522+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Build or simulate a pinching-antenna setup where activation positions are quantized to a grid of spacing $\\delta$ (for example $\\lambda/10$) and the waveguide propagation constant has a few percent uncertainty; run the proposed 3SBT at 28 GHz and compare the final rate to the phase-aligned bound. If the gap does not shrink to near zero as training layers increase while the ideal-continuous codebook does, the perfect-placement assumption is the load-bearing part of the claim.","supporting_citations":[{"cited_title":"Pinching antenna: Using a dielectric waveguide as an antenna,","cited_arxiv_id":null,"evidence_quote":"Introduces the pinching-antenna concept that the paper's system model builds on."},{"cited_title":"Near-field 2D hierarchical beam training for extremely large-scale MIMO,","cited_arxiv_id":null,"evidence_quote":"Supplies the near-field hierarchical 2D beam-training method that the proposed scheme adapts to single-waveguide PASS."},{"cited_title":"Two-stage hierarchical beam training for near-field communications,","cited_arxiv_id":null,"evidence_quote":"Supplies the two-stage angular-and-distance beam-training structure echoed in the three-stage design."},{"cited_title":"Hierarchical codebook- based multiuser beam training for millimeter wave massive MIMO,","cited_arxiv_id":null,"evidence_quote":"Supplies the hierarchical codebook multiuser beam-training idea that justifies avoiding direct channel estimation in the multi-waveguide case."}],"review_version":1}